I have recently started hitting my local velodrome in Herne Hill and it's great fun.
I notice the majority of experienced riders use road pedals such as Look or SPD-SL. The rental bikes just have toe-clips and straps but I, among others, bring along my own pedals which are SPD which work fine.

I noticed when watching the Olympics and other pro velodrome events that the riders appear to have straps on their pedals. What system are they using? Does it combine a road pedal with a strap for extra stiffness or is it a secret custom-made system?